Question

A basketball player is fouled while attempting to make a basket and receives two free throws. The opposing coach believes there is a 32% chance that the player will miss both shots, a 22% chance that he will make one of the shots, and a 46% chance that he will make both shots.

Required:
a. Construct the appropriate probability distribution.
b. What is the probability that he makes no more than one of the shots?
c. What is the probability that he makes at least one of the shots?

Answer 1

To construct the probability distribution, assign probabilities to each possible outcome. The probability that he makes no more than one shot is 54%. The probability that he makes at least one shot is 68%.

Step-by-step explanation:

To construct the probability distribution, we need to assign probabilities to each possible outcome. We have three possible outcomes: missing both shots (32%), making one shot (22%), and making both shots (46%). Therefore, the probability distribution is:

OutcomeProbabilityMiss both shots0.32Make one shot0.22Make both shots0.46

b. To find the probability that he makes no more than one shot, we add the probability of missing both shots and the probability of making one shot: 0.32 + 0.22 = 0.54, or 54%.

c. To find the probability that he makes at least one shot, we subtract the probability of missing both shots: 1 - 0.32 = 0.68, or 68%.